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Abstract <p>A mixed problem for a B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue–Kipriyanov integral measure with weak and strong singularities are introduced. It is proved that there is no energy flow through the singular coordinate hyperplanes, which are the internal boundary of mirror-symmetric domains in Euclidean space. If solutions to these problems exist, their uniqueness is proved.</p>

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On Energy Integrals of a Mixed Problem for a B-Hyperbolic Equation

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • L. N. Lyakhov

摘要

Abstract

A mixed problem for a B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue–Kipriyanov integral measure with weak and strong singularities are introduced. It is proved that there is no energy flow through the singular coordinate hyperplanes, which are the internal boundary of mirror-symmetric domains in Euclidean space. If solutions to these problems exist, their uniqueness is proved.